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Arithmetic Slices 2

1. You are given an array(arr) of integers. 2. You have to find the count of arithmetic slices in the given array. 3. Arithmetic slice is defined as the sub-sequence of an array having all its elements in A.P and length of sub-sequence should be greater than or equal to 3.

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Arithmetic Slices 2

hard

1. You are given an array(arr) of integers. 2. You have to find the count of arithmetic slices in the given array. 3. Arithmetic slice is defined as the sub-sequence of an array having all its elements in A.P and length of sub-sequence should be greater than or equal to 3.

Constraints

1 <= N <= 1000 -10^8 <= arr[i] <= 10^8

Format

Input

A number N arr1 arr2.. N numbers

Output

Check the sample output and question video.

Example

Sample Input

4 1 2 3 4

Sample Output

3

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